The present invention relates to sensors and related methods and computer program products, and more particularly, to mass flow measurement methods, apparatus, computer program products.
Coriolis sensors typically operate by detecting motion of a vibrating conduit that contains a flowing material. Properties associated with the material in the conduit, such as mass flow, density and the like, may be determined by processing signals from motion transducers associated with the conduit, as the vibrational modes of the vibrating material-filled system generally are affected by the combined mass, stiffness and damping characteristics of the containing conduit and the material contained therein.
A typical Coriolis mass flowmeter includes one or more conduits that are connected inline in a pipeline or other transport system and convey material, e.g., fluids, slurries and the like, in the system. Each conduit may be viewed as having a set of natural vibrational modes including, for example, simple bending, torsional, radial and coupled modes. In a typical Coriolis mass flow measurement application, a conduit is excited at resonance in one of its natural vibrational modes as a material flows through the conduit, and motion of the conduit is measured at points spaced along the conduit. Excitation is typically provided by an actuator, e.g., an electromechanical device, such as a voice coil-type driver, that perturbs the conduit in a periodic fashion. Mass flow rate may be determined by measuring time or phase differences between motion at the transducer locations. Exemplary Coriolis mass flowmeters are described in U.S. Pat. No. 4,109,524 to Smith, U.S. Pat. No. 4,491,025 to Smith et al., and U.S. Pat. No. Re. 31,450 to Smith.
The accuracy of Coriolis mass flowmeters may be compromised by the mountings which constrain vibration of the conduit. The affects of these constraints may be reduced by using flowmeter designs that are balanced to reduce effects attributable to external vibration, and by using frequency domain filters, e.g., bandpass filters designed to filter out components of the motion signals away from the excitation frequency. However, mechanical filtering approaches are often limited by mechanical considerations, e.g., material limitations, mounting constraints, weight limitations, size limitations and the like, and frequency domain filtering may be ineffective at removing unwanted vibrational contributions near the excitation frequency.
Conventional Coriolis mass flowmeters typically use a xe2x80x9ccalibration factorxe2x80x9d to scale mass flow rate to time difference or phase measurements to generate a mass flow estimate. Typically, in order to generate a calibration factor, a calibration or xe2x80x9cprovingxe2x80x9d procedure is performed in which a material (e.g., water) is passed through the vibrating conduit of the mass flowmeter in a test fixture while signals produced by the motion transducers of the mass flowmeter are processed to determine time or phase differences. This data is then processed to generate an estimated calibration factor for the meter.
This approach can have several disadvantages. The calibration procedure can be time-consuming, labor-intensive and costly. In addition, because the calibration is typically not performed in the field, it may be subject to inaccuracies due to differences between the test conditions and the conditions of the field, including differences in mounting conditions.
According to embodiments of the present invention, a calibration factor for a parameter sensor including a conduit configured to contain a material and a plurality of motion transducers operative to generate motion signals representing motion of the conduit is determined from a normal modal dynamic characterization of motion of the conduit. The calibration factor may, for example, relate mass flow rate to a spatio-temporal relationship among motion signals produced by the motion transducers, such as a time difference or phase relationship. The calibration factor may be generated, for example, by generating a solution to a modal domain differential equation of motion, and by generating the calibration factor from this solution.
According to some embodiments of the present invention, the normal modal dynamic characterization characterizes motion of the conduit as a function of a modal Coriolis term that describes coupling among a plurality of normal modes of the conduit responsive to mass flow in the conduit. Determination of the calibration factor may be preceded by determining the modal Coriolis term from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit. Modal mass and stiffness terms of the normal modal characterization may be generated using, for example, conventional modal analysis techniques.
For example, in some embodiments, the modal Coriolis term may be determined from a spatial Coriolis characterization that describes motion of a plurality of discrete locations of the conduit in a spatial domain in response to a predetermined mass flow. The modal Coriolis term may be determined from the spatial Coriolis characterization, (e.g., a spatial Coriolis matrix), using a transformation that relates the spatial domain to the plurality of normal modes. The plurality of discrete locations associated with the spatial Coriolis characterization may include locations other than the transducer locations.
The transformation that relates the spatial domain to the plurality of normal modes may be generated from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit. The mode shape function may be determined from a predetermined eigenvalue and a predetermined boundary condition, for example, from an assumption as to a boundary condition to which the conduit will be constrained.
According to other embodiments of the present invention, an orthogonality of a mode shape function for a predetermined mass flow in the conduit is determined in order to determine a modal Coriolis term of a normal modal dynamic characterization of conduit motion. Similar orthogonality determinations can be used to generate modal mass and stiffness terms of the normal modal characterization. Such terms may also be generated using conventional modal analysis techniques.
In other embodiments of the present invention, an estimated spatial response for a plurality of locations of the conduit is generated from a normal modal dynamic characterization, and a calibration factor is generated from the estimated spatial response. For example, a spatio-temporal relationship among movements at a plurality of locations of the conduit, such as a time difference or a phase relationship, may be determined, and the calibration factor may be determined from the spatio-temporal relationship.
In still other embodiments of the present invention, mass flow of a material in a conduit may be determined by determining a calibration factor from a normal modal dynamic characterization of motion of the conduit, generating a plurality of motion signals representing motion of the conduit at a plurality of locations on the conduit, and processing the motion signals according to the determined calibration factor to produce a mass flow estimate. For example, the calibration factor may be determined from a representation of a modal differential equation of motion, as described above. The mass flow estimate may be generated, for example, by determining a spatio-temporal relationship among the plurality of motion signals and applying the calibration factor to the determined spatio-temporal relationship to generate a mass flow estimate.
According to aspects of the present invention, the calibration factor may be determined from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit. The mode shape function may be based on an assumed boundary condition for the conduit. Motion of the conduit may be constrained to induce a boundary condition that approximates the assumed boundary condition, for example, by attaching the conduit to structure or by applying a force to the conduit responsive to motion of the conduit to induce a boundary condition that approximates the assumed boundary condition.
In still other embodiments of the present invention, an apparatus for calibrating a parameter sensor including a conduit configured to contain a material, a plurality of motion transducers operative to generate motion signals representing motion of the conduit and a mass flow estimator circuit operative to estimate mass flow from the motion signals according to a calibration factor is provided. The apparatus includes a calibration factor generator circuit operative to generate a calibration factor from a normal modal dynamic characterization of motion of the conduit, the calibration factor generator circuit including an interface circuit operative to convey the generated calibration factor to the mass flow estimator circuit.
In some embodiments, the calibration factor generator circuit includes a normal modal dynamic characterizer circuit operative to generate a normal modal dynamic characterization of motion of the conduit and a calibration factor determiner circuit operative to determine the calibration factor from the normal modal characterization. The normal modal characterization may be, for example, a representation of a modal differential equation of motion in a modal domain including a plurality of normal modes of motion of the conduit, and the calibration factor determiner circuit may be operative to generate a solution of the modal differential equation of motion from the representation of the modal differential equation of motion and to generate the calibration factor from the solution of the modal differential equation of motion using, for example, the techniques described above. The calibration factor generator circuit may be integrated with the mass flow estimator circuit in, for example, a mass flow sensor apparatus, or may be separately implemented in, for example, test or process control equipment.
In yet other embodiments of the present invention, a mass flow sensor includes a conduit, such as a substantially straight tube, that is configured to contain a material. The mass flow sensor further includes an actuator operative to excite the conduit, a plurality of motion transducers operative to generate motion signals representing motion of the conduit and a mass flow estimator circuit configured to receive the motion signals and operative to generate a mass flow estimate therefrom using a calibration factor derived from a normal modal characterization of motion of the conduit that assumes a predetermined boundary condition for the conduit. Means are provided for constraining motion of the conduit to approximate the predetermined boundary condition.
The means for constraining conduit motion may include, for example, means for attaching the conduit to a structure, such as clamps, welds or other fastening means that attach spaced apart locations of the conduit to a rigid structure. The means for constraining motion of the conduit may also include means for applying a force to the conduit responsive to motion of the conduit to thereby induce a boundary condition that approximates the assumed boundary condition. For example, the means for applying a force to the conduit may include at least two motion transducers operative to generate motion signals representing motion of the conduit, a plurality of actuators operatively associated with the conduit, and a shape control circuit configured to receive motion signals from at least two motion transducers and operative to drive the plurality of actuators responsively thereto.
According to other embodiments of the present invention, a computer program product for characterizing a parameter sensor including a conduit configured to contain a material and a plurality of motion transducers operative to generate motion signals representing motion of the conduit is provided. The computer program product includes computer-readable program code embodied in a computer-readable storage medium, the computer-readable program code including program code for determining a calibration factor for processing motion signals produced by the plurality of motion transducers from a normal modal dynamic characterization of motion of the conduit. The program code for determining a calibration factor may include program code for generating a solution to a modal differential equation of motion in a modal domain including a plurality of normal modes of motion of the conduit, and program code for generating the calibration factor from the generated solution of the modal differential equation of motion. The normal modal dynamic characterization may characterize motion of the conduit as a function of a modal Coriolis term that describes coupling among a plurality of normal modes of the conduit responsive to mass flow in the conduit. The computer readable program code may include program code for determining the modal Coriolis term from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit.